Mathematics, 01.04.2020 20:47 Braxtonw875

C(x) = 0.000002x3 − 0.03x2 + 400x + 80,000 where C(x) denotes the total cost incurred in producing x sets. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula

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Answer from: QueensQueens

The producer will have maximum profit when x is 5000.

Step-by-step explanation:

Given C(x) = 0.000002x³ - 0.03x² + 400x + 80000

To find the level of production that will yield the maximum profit for the manufacturer, firstly, we differentiate C(x) to obtain C'(x), we then set the resulting quadratic expression to zero and solve. Whichever of the two values obtained from the quadratic equation will be tested to see what we want to find.

Differentiate C(x)

C'(x) = 3(0.000002)x² - 2(0.03)x + 400

= 0.000006x² - 0.06x + 400

Set C'(x) = 0

0.000006x² - 0.06x + 400 = 0

Solve using quadratic formula.

x = [-b ± √(b² - 4ac)]/2a

a = 0.000006

b = -0.06

c = 400

x = [-(-0.06) ± √((-0.06)² - 4(0.000006 × 400)]/2(0.000006)

= [0.06 ± √(0.0036 - 0.0096]/0.000012

= (0.06/0.000012) ± i√(0.006)/0.000012

= 5000 ± 6454.97i

x = 5000 + 6454.97i

x = 5000 - 6454.97i

Answer from: Quest

45 this is because of the agarose

Answer from: Quest

the speed is $135$ miles per hour > is false

step-by-step explanation:

we know that

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

$y/x=k$

for the point $(1.5,90)$

substitute the values of x and y

$k=90/1.5=60\ miles/hour$

the linear equation is equal to

$y=60x$

statements

case a) it takes $2$ hours to go $120$ miles

the statement is true

because

substitute

for $x=2$

find the value of y in the linear equation

$y=60(2)=120\ miles$ > is correct

case b) the speed is $135$ miles per hour

the statement is false

because the speed is $60\ miles/hour$

case c) the unit rate for the trip is $60\ miles/hour$

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took $20$ minutes to go the first $20$ miles

the statement is true

because

substitute

for $x=20\ minutes=(1/3)\ hour$

find the value of y in the linear equation

$y=60(1/3)=20\ miles$ > is correct

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C(x) = 0.000002x3 − 0.03x2 + 400x + 80,000 where C(x) denotes the total cost incurred in producing x...

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